Priority Queueing System with Many Types of Requests and Restricted Processor Sharing

A priority queueing model with many types of requests and restricted processor sharing is considered. A novel discipline of requests admission and service is proposed. This discipline assumes restriction of the bandwidth (capacity) of the server and the number of requests that can receive service in the system at the same time. This discipline is some kind of realistic hybrid of the traditional discipline of service in a multi-server system and the discipline of the limited processor sharing. The requests of the highest priority can push out from the service the low priority requests. Therefore, the important problem is fitting of the number of requests that can receive service at the same time to the bandwidth of the server. This problem is solved via construction and analysis of a multi-dimensional Markov chain describing operation of the system under any fixed set of the system parameters.